Theoretical and numerical studies of crack initiation and propagation in rock masses under freezing pressure and far-field stress

Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Effects of gully terrain on stress field distribution and ground pressure behavior in shallow seam mining

This study proposes a novel approach to study stress field distribution and overlying ground pressure behavior in shallow seam mining in gully terrain.This approach combines numerical simulations and field tests based on the conditions of gully terrain in the Chuancao Gedan Mine.The effects of gully terrain on the in situ stress field of coal beds can be identified by the ratio of self-weight stress to vertical stress(η) at the location corresponding to the maximum vertical stress.Based on the function η =j(h),the effect of gully terrain on the stress field of overlying strata of the entire field can be characterized as a significantly affected area,moderately affected area,or non-affected area.Working face 6106 in the Chuancao Gedan Mine had a coal bed Jepth <80 m and was located in what was identified as a significantly affected area.Hence,mining may cause sliding of the gully slope and increased loading(including significant dynamic loading) on the roof strata.Field tests suggest that significant dynamic pressures were observed at the body and foot of the gully slope,and that dynamic loadings were observed upslope of the working face expansion,provided that the expanding direction of the working face is parallel to the gully.

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.

Study on Swell Pressure Stress of Bentonite in Geosynthetic Clay Liners

The geosynthetic clay liner （GCL） is a kind of waterproofing material used widely in engineering. The waterproof mechanism is understood in terms of bentonite particles becoming water-obstruct colloid layers after they sorb water and swell. The swell pressure stress, however, has not been determined directly till now. In our experiment, swell pressure stress of the GCL under saturated water-sorbing condition was measured directly using a custom-made instrument. The results show that （1） the instrument designed by the authors performs satisfactorily and the test results are reproducible; and （2） the trend line of swell pressure stress variation with time can be divided into three segments. The first segment is characterized by a quick increase of the swell force in the first 0-50 hours. The swell pressure stress increases by 7.00×10^-4-1.00×10^-3 MPa/h. The second segment shows a slow increase of the swell pressure stress from the 50th to 1730th hour. The swell force increases by 7.54×10^-6-2.02×10^-5 MPa/h. The third segment is characterized by a little variation in swell pressure stress after 1730 hours. In this segment, the average value of the swell pressure stress measurements is 0.0719 MPa and the maximum value is 0.0729 MPa. It is suggested that the swell pressure stress is mainly raised by water entering pores among montmorillonite particles and interstitial layers in individual montmorillonite crystals, leading to an increase of volume.

Effects of Pressure Stress Work and Viscous Dissipation in Mixed Convection Flow Along a Vertical Flat Plate

The Effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical fiat plate have been investigated. The results are obtained by transforming the governing system of boundary layer equations into a system of non-dimensional equations and by applying implicit finite difference method together with Newton＇s linearization approximation. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction co-efficient and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters.

Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure

To reveal the water inrush mechanics of underground deep rock mass subjected to dynamic disturbance such as blasting, compression-shear rock crack initiation rule and the evolution of crack tip stress intensity factor are analyzed under static-dynamic loading and seepage water pressure on the basis of theoretical deduction and experimental research. It is shown that the major influence factors of the crack tip stress intensity factor are seepage pressure, dynamic load, static stress and crack angle. The existence of seepage water pressure aggravates propagation of branch cracks. With the seepage pressure increasing, the branch crack experiences unstable extension from stable propagation. The dynamic load in the direction of maximum main stress increases type I crack tip stress intensity factor and its influence on type II crack intensity factor is related with crack angle and material property. Crack initiation angle changes with the dynamic load. The initial crack initiation angle of type I dynamic crack fracture is 70.5°. The compression-shear crack initial strength is related to seepage pressure, confining pressure, and dynamic load. Experimental results verify that the initial crack strength increases with the confining pressure increasing, and decreases with the seepage pressure increasing.

MATHEMATIC MODEL AND ANALYTIC SOLUTION FOR CYLINDER SUBJECT TO UNEVEN PRESSURES

According to the inverse solution of elasticity mechanics, a stress function is constructed which meets the space biharmonic equation, this stress functions is about cubic function pressure on the inner and outer surfaces of cylinder. When borderline condition that is predigested according to the Saint-Venant＇s theory is joined, an equation suit is constructed which meets both the biharmonic equations and the boundary conditions. Furthermore, its analytic solution is deduced with Matlab. When this theory is applied to hydraulic bulging rollers, the experimental results inosculate with the theoretic calculation. Simultaneously, the limit along the axis invariable direction is given and the famous Lame solution can be induced from this limit. The above work paves the way for mathematic model building of hollow cylinder and for the analytic solution of hollow cvlinder with randomly uneven pressure.

Theoretical analysis of influencing factors on resistance in the process of gas migration in coal seams

Inspired by previous resistance models for porous media, a resistance expression of gas migration within coal seams based on the ideal matchstick geometry, combined with the Darcy equation and the modified Poiseuille equation is proposed. The resistance to gas migration is generally dynamic because of the variations in adsorption swelling and matrix shrinkage. Due to the limitations of experimental conditions,only a theoretical expression of resistance to gas migration in coal is deduced, and the impacts of tortuosity, effective stress and pore pressure on the resistance are then considered. To validate the proposed expression, previous data from other researchers are adopted for the history matching exercise, and the agreement between the two is good.

Numerical analysis of elastic coated solids in line contact

A line contact model of elastic coated solids is presented based on the influence coefficients(ICs) of surface displacement and stresses of coating-substrate system and the traditional contact model. The ICs of displacement and stresses are obtained from their corresponding frequency response functions(FRF) by using a conversion method based on fast Fourier transformation(FFT). The contact pressure and the stress field in the subsurface are obtained by employing conjugate gradient method(CGM) and discrete convolution fast Fourier transformation(DC-FFT). Comparison of the contact pressure and subsurface stresses obtained by the numerical method with the exact analytical solutions for Hertz contact is conducted, and the results show that the numerical solution has a very high accuracy and verify the validity of the contact model. The effect of the stiffness and thickness of coatings is further numerically studied. The result shows that the effects on contact pressure and contact width are opposite for hard and soft coatings and are intensified with the increase of coating thickness; the locations of crack initiation and propagation are different for soft and hard coatings; the risk of cracks and delaminations of coatings can be brought down by improving the lubrication condition or optimizing the non-dimensional parameter h/bh. This research offers a tool to numerically analyze the problem of elastic coated solids in line contact and make the blindness and randomness of trial-type coating design less.

Deformation transition of intact coal induced by gas injection

Gas migration in coal bed is a multiple-physical process, of which not only includes gas desorption/diffusion through coal matrix and gas Darcy flow through the cleat system, but also results in deformation of solid coal. Especially for enhanced coal bed methane(ECBM) and CO2 capture and sequestration(CCS), gas injection is mainly controlled by the gas diffusivity in the coal matrix and coal permeability.Although the relevant coal permeability models have been frequently developed, how the dual-porosity system of coal affects gas adsorption/diffusion is still poorly understood. In this paper, a series of experiments were carried out in order to investigate deformation evolution of intact coal subjected to hydrostatic pressure of different gases(including pure H2, N2 and CO2) under isotherm injection. In the testing process, the coal strain and injected gas pressure were measured simultaneously. The results show that the pressure of non-adsorptive helium remained unchanged throughout the isothermal injection process, in which the volumetric strain of the coal shrinked firstly and maintained unchanged at lower isobaric pressure. With the injected pressure increasing, the coal volume underwent a transition from shrinking to recovery(still less than initial volume of the coal). In contrast, N2 injection caused the coal to shrink firstly and then recover with decreasing gas pressure. The recovery volume was larger than the initial volume due to adsorption-induced swelling. For the case of CO2 injection, although the stronger adsorption effect could result in swelling of the solid coal, the presence of higher gas pressure appears to contribute the swelling coal to shrink. These results indicate that the evolution of coal deformation is time dependent throughout the migration of injected gas. From the mechanical characteristics of poroelastical materials, distribution of pore pressure within the coal is to vary with the gas injection,during which the pore pressure in the cleats will rapidly increase, in contrast, the pore pressure in the matrix will hysteretically elevate. Such a difference on changes of pore pressure between the cleats and the matrix will contribute to the shrinkage of the matrix as a result of initially greater effective stress.Besides, both gas-adsorption-induced swelling and decreasing effective stress also control the coal deformation transition. This work gives us an insight into investigation on influence of effective stress on coal-gas interaction.

Influence of residual stresses on failure pressure of cylindrical pressure vessels

The utilization of pressure vessels in aerospace applications is manifold.In this work,fnite element analysis（FEA）has been carried out using ANSYS software package with 2D axisymmetric model to access the failure pressure of cylindrical pressure vessel made of ASTM A36 carbon steel having weld-induced residual stresses.To fnd out the effect of residual stresses on failure pressure,frst an elasto-plastic analysis is performed to fnd out the failure pressure of pressure vessel not having residual stresses.Then a thermo-mechanical fnite element analysis is performed to assess the residual stresses developed in the pressure vessel during welding.Finally one more elasto-plastic analysis is performed to assess the effect of residual stresses on failure pressure of the pressure vessel having residual stresses.This analysis indicates reduction in the failure pressure due to unfavorable residual stresses.

Forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by CNTs based on MCST with temperature-variable material properties

In this study, free and forced vibration analysis of nano-composite rotating pressurized microbeam reinforced by carbon nanotubes （CNTs） under magnetic field based on modify couple stress theory （MCST） with temperature-variable material propertiesis presented. Also, the boundary conditions at two ends of nano-composite rotating pressurized microbeam reinforced by CNTs are considered as simply supported. The governing equations are obtained based on the Hamilton＇s principle and then computed these equations by using Navier＇s solution. The magnetic field is inserted in the thickness direction of the nano-composite microbeam. The effects of various parameters such as angular velocity, temperature changes, and pressure between of the inside and outside, the magnetic field, material length scale parameter, and volume fraction of nanocomposite microbeam on the natural frequency and response systemare studied. The results show that with increasing volume fraction of nano-composite microbeam, thickness, material length scale parameter, and magnetic fields, the natural frequency increases. The results of this research can be used for optimization of micro-structures and manufacturing sensors, displacement fluid, and drug delivery.

Dynamic Mechanical Characteristics and Damage Evolution Model of Granite

By using the technique of the split Hopkinson pressure bar（ SHPB）,impact tests at different stress wavelengths（ 0. 8-2. 0 m） and strain rates（ 20-120 s^（-1）） were conducted to study the dynamic mechanical properties and damage accumulation evolution lawof granite. Test results showthat the dynamic compressive strength and strain rate of granite have a significantly exponential correlation;the relationship between peak strain and strain rate is approximately linear,and the increase of wavelengths generally makes the level of peak strain uplift. The multiple-impacts test at a lowstrain rate indicates that at the same wavelength,the cumulative damage of granite shows an exponential increasing form with the increase of strain rate; when keeping the increase of strain rate constant and increasing the stress wavelength,the damage accumulation effect of granite is intensified and still shows an exponential increasing form; under the effect of multiple impacts,the damage development trend of granite is similar overall,but the increase rate is accelerating. Therefore the damage evolution model was established on the basis of the exponential function while the physical meaning of parameters in the model was determined. The model can reflect the effect of the wave parameters and multiple impacts. The validity of the model and the physical meaning of the parameters were verified by the test,which further offer a reference for correlational research and engineering application for the granite.

Interactive response of photosynthetic characteristics in Haloxylon ammodendron and Hedysarum scoparium exposed to soil water and air vapor pressure deficits

C4 plants possess better drought tolerance than C3 plants. However, Hedysarum scoparium, a C3 species, is dominant and widely distributed in the desert areas of northwestern China due to its strong drought tolerance. This study compared it with Haloxylon ammodendron, a C4 species, regarding the interactive effects of drought stress and different leaf–air vapor pressure deficits. Variables of interest included gas exchange, the activity levels of key C4 photosynthetic enzymes, and cellular anatomy. In both species, gas exchange parameters were more sensitive to high vapor pressure deficit than to strong water stress, and the net CO2 assimilation rate（A n） was enhanced as vapor pressure deficits increased. A close relationship between A n and stomatal conductance（g s） suggested that the species shared a similar response mechanism. In H. ammodendron, the activity levels of key C4 enzymes were higher, including those of phosphoenolpyruvate carboxylase（PEPC） and nicotinamide adenine dinucleotide phosphate-malate enzyme（NADP-ME）, whereas in H. scoparium, the activity level of nicotinamide adenine dinucleotide-malate enzyme（NAD-ME） was higher.Meanwhile, H. scoparium utilized adaptive structural features, including a larger relative vessel area and a shorter distance from vein to stomata, which facilitated the movement of water. These findings implied that some C4 biochemical pathways were present in H. scoparium to respond to environmental challenges.

Optimum Heating of Thick-Walled Pressure Components Assuming a Quasi-steady State of Temperature Distribution

As a result of the development of wind farms,the gas- steam blocks,which shall quickly ensure energy supply in case the wind velocity is too low,are introduced to the energy system.To shorten the start-up time of the gas-steam and conventional blocks,the structure of the basic components of the blocks are changed,e.g.by reducing the diameter of the boiler,the thickness of its wall is also reduced.The attempts were also made to revise the currently binding TRD 301 regulations,replacing them by the EN 12952-3 European Standard,to reduce the allowable heating and cooling rates of thick walled boiler components.The basic assumption,on which the boiler regulations allowing to calculate the allowable temperature change rates of pressure components were based,was the quasi- steady state of the temperature field in the simple shaped component,such as a slab,cylindrical or spherical wall.

ACOUSTOELASTIC THEORY FOR FLUID-SATURATED POROUS MEDIA

Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.